Related papers: On the generalizations of global dimensions and si…

In this note we first study regular $\mathbb{Z}$-graded local rings. We characterize commutative noetherian regular $\mathbb{Z}$-graded local rings in similar ways as in the usual local case. Then, we characterize graded isolated…

We review and systematize recent attempts to canonically quantize general relativity in 2+1 dimensions, defined on space-times $\R\times\Sigma^g$, where $\Sigma^g$ is a compact Riemann surface of genus $g$. The emphasis is on quantizations…

Let $R$ be a commutative ring and $\Gamma$ be an infinite discrete group. The algebraic $K$-theory of the group ring $R[\Gamma]$ is an important object of computation in geometric topology and number theory. When the group ring is…

Chern-Simons models for gravity are interesting because they provide with a truly gauge-invariant action principle in the fiber-bundle sense. So far, their main drawback has largely been the perceived remoteness from standard General…

In this paper we classify global dimensions of the category algebras of some finite categories, including finite truncations of the categories $FI$, $FI_G$, $FI_d$, $OI$, $OI_G$, $OI_d$ and $VI$

G\"{o}del universe is a homogeneous rotating dust with negative $\Lambda$ which is a direct product of three dimensional pure rotation metric with a line. We would generalize it to higher dimensions for Einstein and pure Lovelock gravity…

If D is a category and k is a commutative ring, the functors from D to k-Mod can be thought of as representations of D. By definition, D is dimension zero over k if its finitely generated representations have finite length. We characterize…

Let $R$ be a commutative $F$-algebra, where $F$ is a field of characteristic 0, satisfying the following conditions: $R$ is equidimensional of dimension $n$, every residual field with respect to a maximal ideal is an algebraic extension of…

This paper introduces the concept of a generic finite set, and points out that a consistent and significant interpretation of the grossone notation of Yarolslav D. Sergeyev is that of a generic natural number. This means that the grossone…

Let $(R,\m,k)$ be a commutative noetherian local ring of Krull dimension $d$. We prove that the cohomology annihilator $\ca(R)$ of $R$ is $\m$-primary if and only if for some $n\ge0$ the $n$-th syzygies in $\mod R$ are constructed from…

For a commutative Gorenstein Noetherian ring $R$, we construct an affine scheme $X$ solely from DG singularity category $S_{dg}(R)$ of $R$ such that there is a finite surjective morphism $X \rightarrow \mathrm{Spec}(R /I)$, where…

Let $\mathbf{k}$ be field of arbitrary characteristic and let $\Lambda$ be a finite dimensional $\mathbf{k}$-algebra. From results previously obtained by F.M Bleher and the author, it follows that if $V^\bullet$ is an object of the bounded…

We investigate the homological behaviour of compactly generated triangulated categories under separable extensions. We show that homological invariants (finiteness of global dimension, gorensteinness and regularity) are preserved under such…

We disprove two (unpublished) conjectures of Kontsevich which state generalized versions of categorical Hodge-to-de Rham degeneration for smooth and for proper DG categories (but not smooth and proper, in which case degeneration is proved…

This thesis gives a complete description of the Grothendieck group and divisor class group for large families of two and three dimensional singularities. The main results presented throughout, and summarised in Theorem 8.1.1, give an…

First we study the Gorenstein cohomological dimension ${\rm Gcd}_RG$ of groups $G$ over coefficient rings $R$, under changes of groups and rings; a characterization for finiteness of ${\rm Gcd}_RG$ is given. Some results in literature…

We introduce the notion of integrality of Grothendieck categories as a simultaneous generalization of the primeness of noncommutative noetherian rings and the integrality of locally noetherian schemes. Two different spaces associated to a…

Global visibility of naked singularities is analyzed here for a class of spherically symmetric spacetimes, extending previous studies - limited to inhomogeneous dust cloud collapse - to more physical valid situations in which pressures are…

In this paper, we introduce several notions of "dimension" of a finite group, involving sizes of generating sets and certain configurations of maximal subgroups. We focus on the inequality $m(G) \leq \mathrm{MaxDim}(G)$, giving a family of…

We consider a static, axially symmetric, and asymptotically flat exact solution of the Einstein vacuum equations, known as the gamma metric. This is characterized by two constant parameters $m$ and $\gamma$. We find that the total energy…